自适应非结构有限元MT二维起伏地形正反演研究

在山区进行MT勘探时,用规则网格有限元方法模拟起伏地形会受到限制.本文采用非结构三角网格可以有效地模拟任意二维地质结构,如起伏地形、倾斜岩层和多尺度构造等.正演引入自适应有限元方法,其在网格剖分过程中能根据单元误差自动细化网格,保证了正演结果的精度.将自适应有限元与Occam算法结合,且引用并行处理技术提高正反演计算速度.通过对比两个理论模型,讨论了地形对MT正演响应的影响;其次进行了不同地电模型带地形反演展示了本文算法的正确性和适用性;最后将该方法应用于实测MT数据处理,证明了自适应非结构有限元方法是复杂地形下处理MT数据的有力工具.     

基于非结构网格的电阻率三维带地形反演

地表起伏地形在野外矿产资源勘察中不可避免,其对直流电阻率法勘探影响巨大.近年来,电阻率三维正演取得诸多进展,特别是应用非结构网格我们能够进行任意复杂地形和几何模型的电阻率三维数值模拟,但面向实际应用的起伏地形下电阻率三维反演依然困难.本文基于非结构化四面体网格,并考虑到应用GPS/GNSS时,区域地球物理调查中可非规则布设测网的实际特点,实现了任意地形(平坦或起伏)条件下、任意布设的偶极-偶极视电阻率数据的不完全Gauss-Newton三维反演.合成数据的反演结果表明了方法的有效性,可应用于复杂野外环境下的三维电法勘探.     

基于有限差分正演的带地形三维大地电磁反演方法

本研究实现了一套基于有限差分（FD）方法的大地电磁测深数据带地形三维反演算法及代码.其中,在大地电磁场正演数值模拟方面,开发了起伏地形条件下基于交错网格剖分、有限差分方法的大地电磁测深三维正演代码;在满足平面波场假设的前提下,使用长方体网格剖分模拟三维起伏地形,实现了带地形三维正演计算;并设计理论模型进行试算,经试算结果与前人的有限元法计算结果对比,验证了所研发的带地形三维正演计算的正确性与可靠性.在反演方面,本研究基于非线性共轭梯度方法编写了大地电磁测深带地形三维反演代码,试验了不同的共轭梯度搜索因子β,避免了目标函数对海森矩阵（参数二次导数矩阵）的显式计算和存储,初步实现了大地电磁资料的带地形三维反演.最后,对一系列理论模型进行正演计算,利用其生成的合成数据模拟实测数据进行反演,并与现有的不带地形大地电磁测深三维反演结果比较,检验了所研发的带地形三维反演计算的可靠性与稳定性.     

基于矢量有限元的带地形大地电磁三维反演研究

研究了基于矢量有限元方法的大地电磁带地形三维反演算法并开发了三维反演计算程序代码.在大地电磁场正演数值模拟方面,采用并行直接稀疏求解器PARDISO且无需进行散度校正的快速正演方案,对典型地形模型,在中等规模计算条件下,与双共轭梯度法(BICG)计算结果比较,发现PARDISO比BICG快10倍以上;通过理论模型试算,并与前人的有限元法计算结果对比,验证了带地形三维正演计算程序的正确性.在反演方面,本研究基于共轭梯度方法编写了大地电磁带地形三维反演代码,为了避免直接求取雅可比矩阵,将反演中的雅可比矩阵计算问题转为求解两次“拟正演”问题,进而将PARDISO的快速正演方案应用于“拟正演”问题的求解,以提高反演计算效率.利用开发的反演算法对多个带地形地电模型的合成数据进行了三维反演,反演结果能很好地重现理论模型的电性结构,验证了本文开发的三维反演算法的正确性和可靠性.最后,利用该算法反演了某矿区大地电磁实测数据,反演得到的三维电性结构清晰地反映了研究区的地电特征,将反演结果与该区已有地质资料结合进行解释,应用效果明显,进一步验证了本文算法的有效性.     

三维电阻率测深数据Zohdy近似反演方法

Zohdy方法近似反演三维电阻率测深数据。正演计算采用有限单元法。反演初始模型由测量视电阻率数据给出。通过比较实测视电阻率值和预测模型计算的视电阻率值对数差来修改模型网格电阻率．为了解决任意电极距测深数据的反演,采用大、小双网格剖分。大网格反映地下电性分布情况。小网格用于实际有限元正演计算．在电阻率调整公式中加入一个迭代系数,能够加快收敛速度．并对加5％随机噪声的模型理论视电阻率测深断面数据进行反演,得到的电阻率分布与模型电阻率基本一致．     

2.5维电导率正交各向异性海洋可控源电磁等参有限元数值模拟

本文实现了2.5维电导率正交各向异性海洋可控源电磁等参有限元数值模拟.利用傅里叶变换导出了电导率正交各向异性2.5维海洋可控源电磁法波数域电磁场耦合方程,采用伽里金加权余量法推导了相应的有限元方程;采用任意四边形单元对研究区域进行剖分,在单元中进行双二次插值,将有限元方程化为线性代数方程组;最后,求解线性方程组并进行反傅里叶变换获得空间域电磁场值.这个方法可以模拟海底起伏地形条件下地下任意形状电导率正交各向异性的复杂模型.与一维模型的数值模拟结果对比表明,电磁场数值解与解析解吻合.二维模型的计算结果与二维自适应非结构有限元模拟结果也吻合.水平海底二维地电模型考察了不同各向异性系数对海洋可控源电磁响应的影响特征.海底起伏地形地电模型的数值结果表明,电导率各向异性对海洋可控源电磁响应影响明显,有可能淹没海底地形和高阻油气藏引起的异常.     

基于改进Krylov子空间算法的井中激电反演

井中激电是二次找矿重要的地球物理勘探手段,快速而稳定的正反演算法有助于方法的推广和应用.本文在正演模拟中,给出了考虑井眼影响下的网格剖分方式;用右端项校正技术减小边界效应和源点奇异性引起的模拟误差;并采用循环Krylov子空间算法提高多线性方程组的求解效率.反演用Gauss-Newton法结合Jacobian-free Krylov迭代求解技术,给出了Jacobian矩阵向量积的简化计算方法;用不精确预处理共轭梯度法对模型修正量方程近似求解以减少计算量;采用不同于正演的反演网格剖分降低不适定性.数值算例验证了相关算法的有效性和可靠性.     

基于非规则网格声波正演的时间域全波形反演

全波形反演是地震资料处理中速度建模的有力工具,相比层析成像等速度建模方法它能够得到速度场的更高频成分.本文给出了基于声波方程格子法正演的时间域全波形反演方法,该方法用非规则、非结构化的三角网格来离散计算区域及模型参数,能实现网格粒度与反演分辨率在空间上的自动匹配,内存需求少,计算效率高;采用L-BFGS优化方法,以分频段变网格的方式实施多尺度反演.以二维Overthrust模型进行了速度反演数值测试,显示了该方法的高效性和潜力.     

时间域全波场各向异性弹性参数反演

从各向异性弹性波的有限元正演方程出发 ,导出了反问题中时间域雅可比矩阵求解的计算公式 .它具有与时间域有限元正演方程相同的表达形式 ,故可通过有限元正演计算来获得雅可比矩阵 .研究了有限元正演算法的效率和精度、吸收边界条件等方面的问题 ,以提高反演系统的效率和精度 .在此基础上 ,实现了叠前全波场各向异性弹性参数反演 .计算表明 ,在初始模型偏离真实模型较大的情况下 ,层状模型和横向不均匀模型的反演结果均能准确地收敛到真实模型上 .     

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.     

基于非结构有限元的时间域海洋电磁三维反演

海洋电磁法是一种有效的钻前储层评价手段,可识别出海底构造是否储油气,从而减少干井率降低勘探成本.近年来,频率域三维海洋电磁反演得到了快速发展,但受到空气波的影响,其在浅海环境中无法取得很好的效果.为解决这一问题,本文研究时间域海洋电磁数据三维正反演.正演模拟和计算中,我们选择基于非结构网格的矢量有限元方法.该算法中空间离散采用非结构四面体网格,可很好地拟合复杂海底地形条件和地下复杂结构;而对于时间离散,我们采用无条件稳定的后推欧拉方法,以确保任意时间步长数值计算的稳定性.反演计算中,灵敏度信息采用伴随正演隐式进行计算;同时,依据时间域反演方法的特点采用L-BFGS方法计算模型修正量.通过利用合成数据反演结果证明了本文提出的三维时间域反演方法可用于复杂海底环境,特别是在浅海环境下的有效性.     

基于紧凑存储的任意四边形网格有限元法地震波场数值模拟

采用有限元法精确模拟复杂介质条件下的地震波场,一般采用三角单元,但在节点数相同的情况下,三角单元的计算精度不如矩形单元高,采用三角单元模拟复杂界面时,编制确定结构刚度矩阵非零元素位置的程序也较为麻烦。采用矩形单元离散含有倾斜或起伏界面的地质模型时,无法避免绕射噪声,若加密网格又会增加计算量。为此,本文基于任意四边形单元模拟声波的传播,在倾斜或起伏界面条件下,可以有效避免因离散引起的“阶梯状”界面,在不增加计算量以及内存占用的前提下,有效地消除离散绕射噪声。采用对角的集中质量矩阵代替一致质量矩阵,避免矩阵的求逆运算,从而提高显式有限元法的计算效率;对结构刚度矩阵采用紧凑存储格式,每一行需要存储的元素最多为5个,同时零元素不参与运算,既减少内存的占用,又极大地提高计算效率。      

Modelling and inversion of electromagnetic data using an approximate plate model

This paper presents a computational method for the interpretation of electromagnetic (EM) profile data in the frequency domain using a thin plate model within a two-layer earth. The modelling method is based on an integral equation formulation, where the conductor is represented by a lattice structure composed of two-dimensional surface elements. Several approximations are used to simplify the theoretical basis and to decrease the computation time. The simple parametric model allows efficient use of optimization methods. We employ a linearized inversion scheme based on singular value decomposition and adaptive damping. The new forward computation method and the parameter optimization are combined in the computer program, emplates . The modelling examples demonstrate that the approximate method is capable of describing the characteristic behaviour of the EM response of a thin plate-like conductor in conductive surroundings. The efficacy of the inversion is demonstrated using both synthetic and field data. An optional depth compensation method is used to improve the interpreted values of the depth of burial. The results show that the method is cost effective and suitable for interactive interpretation of EM data.     

Inversion of magnetotelluric data in the presence of strong bathymetry/topography

We describe an algorithm for inverting magnetotelluric (MT) data in the presence of strong bathymetry or topography. Instead of correcting distortions due to bathymetry or topography we incorporate them directly into the inversion. To achieve a high accuracy in computing MT responses we use finite‐difference approximations that permit sloping discrete boundaries inside model elements. The same approach is applicable to any seafloor electromagnetic calculation and can also be used to incorporate steep topography on land. We test our approach on various topographic features and compare our results to that of a finite element approach. Finally, we present inversion examples that illustrate the effectiveness of our inversion algorithm in recovering true subsurface structures in the presence of strong bathymetry and topography.     

面向目标自适应三维大地电磁正演模拟

本文将面向目标的自适应算法应用于三维大地电磁数值模拟.使用基于非结构网格的矢量有限单元法对起伏地表大地电磁正演模拟问题进行求解.使用利用垂向电流密度在物性界面上的连续性对后验误差进行估算的算法指导网格优化.由于全局自适应算法针对观测点优化网格的能力较差,本文通过求解正演问题的对偶问题计算后验误差的加权系数,并对相关加权系数进行改进,从而实现了面向目标的自适应算法.与传统基于结构化网格的电磁正演算法相比,采用非结构网格能够更好地拟合起伏地表和地下不规则异常体.由于使用了面向目标的自适应算法,本文能够使用更少的网格达到较高的计算精度.通过对比本文模拟结果与半空间响应和全局自适应算法计算结果,并通过对比使用改进前和改进后加权系数得到的网格剖分结果验证了本文算法的有效性.     

Interactive 3D forward modeling of total field surface and three-component borehole magnetic data for the Daye iron-ore deposit (Central China)

The ground magnetic response of deep ore bodies in the Daye iron-ore deposit is relatively weak, and sometimes concealed by the strong magnetic background of shallower sources. Apart from the low-quality ground magnetic data, another critical problem for reconstructing the deep skarn-type ore bodies is developing a versatile inversion scheme that can simultaneously resolve 3D sources with arbitrary shapes. In this case, we resort to interactive 3D forward modeling solution with the joint use of two data sets-total field surface and three-component borehole magnetic data. Joint inversion of the two data sets is expected to help resolve the ambiguity associated with either data set and greatly reduces the nonuniqueness of the magnetic inversion. Such nonuniqueness is especially severe when a 3-D distribution of magnetic susceptibility, instead of a simple body, is sought from the inversion.In this paper, we calculate the magnetic field on the surface and in the borehole caused by 3D arbitrarily-shaped bodies with the triple integral method. The complex 3D magnetic sources having arbitrary shapes are constructed with cross-sections, termination points and facets in our visualization technology. We specify, interactively and in a user-friendly environment, the outline of the sources in terms of geometric elements and their magnetic parameters. The method automatically fits the observations within a prescribed precision. If dissatisfied, the user can redefine the model parameters and proceed to a new inversion. The method's ability to interpret a complicated 3D geologic environment is demonstrated on synthetic models and real data profiles in the Daye iron-ore deposit in central China. The interactive forward modeling results in all tests demonstrate a good correlation of estimated magnetic sources with corresponding known geologic features.     

2-D Frequency-domain Waveform Inversion of Coupled Acoustic-Elastic Media with an Irregular Interface

In order to correctly interpret marine exploration data, which contain many elastic signals such as S waves, surface waves and converted waves, we have developed both a frequency-domain modeling algorithm for acoustic-elastic coupled media with an irregular interface, and the corresponding waveform inversion algorithm. By applying the continuity condition between acoustic (fluid) and elastic (solid) media, wave propagation can be properly simulated throughout the coupled domain. The arbitrary interface is represented by tessellating square and triangular finite elements. Although the resulting complex impedance matrix generated by finite element methods for the acoustic-elastic coupled wave equation is asymmetric, we can exploit the usual back-propagation algorithm used in the frequency domain through modern sparse matrix technology. By running numerical experiments on a synthetic model, we demonstrate that our inversion algorithm can successfully recover P- and S-wave velocity and density models from marine exploration data (pressure data only).     

二维水平电偶极变频测深阻抗视电阻率的有限元正演计算

在二维地电断面情况下,电偶源变频测深阻抗视电阻率的有限元计算,存在着两个困难:一个是对源的处理;另一个是边界条件的确定。本文提出了解决这两个问题的方法,构成了含源波动方程的边值问题,用有限元法求出了相应的电磁场分量,从而计算出二维地电断面的阻抗视电阻率。对各种地电断面计算的结果表明,计算方法是正确的,可对实际地电断面进行有限元模拟,求得其电磁响应。     

复杂介质有限元法2.5维可控源音频大地电磁法数值模拟

利用有限元2.5维可控源音频大地电磁法（简称CSAMT）数值模拟方法,对100Ωm均匀半空间介质中有限长度的电偶极源产生的电场、磁场及视电阻率、相位特征进行了数值模拟,研究了场的空间变化规律. 在一个象限中,场的特征存在双叶现象,当收发距大于4个趋肤深度时,电阻率较接近介质真实的电阻率,这些结果为观测系统和收发距的选择提供了依据. 波数域场的特征表明,低波数对源的贡献占较大的比例. 有限元法2.5维CSAMT数值模拟的优势在于能较准确地获得复杂介质结构的波场特征. 本文结合直立异常体、倾斜异常体及断陷模型对CSAMT电阻率、相位剖面特征及频率曲线特征的可靠性进行了研究. 数值模拟结果直观地给出了异常体的剖面异常形态. 通过对比研究异常体的剖面异常形态和半空间场的特征进一步说明本文方法和软件在模拟复杂介质结构场特征时是可靠的. 这为认识观测数据,指导反演解释提供了较好的依据.     

P-wave Tomography in Inhomogeneous Orthorhombic Media

— A P-wave tomographic method for 3-D complex media (3-D distribution of elastic parameters and curved interfaces) with orthorhombic symmetry is presented in this paper. The technique uses an iterative linear approach to the nonlinear travel-time inversion problem. The hypothesis of orthorhombic anisotropy and 3-D inhomogeneity increases the set of parameters describing the model dramatically compared to the isotropic case. Assuming a Factorized Anisotropic Inhomogeneous (FAI) medium and weak anisotropy, we solve the forward problem by a perturbation approach. We use a finite element approach in which the FAI medium is divided into a set of elements with polynomial elastic parameter distributions. Inside each element, analytical expressions for rays and travel times, valid to first-order, are given for P waves in orthorhombic inhomogeneous media. More complex media can be modeled by introducing interfaces separating FAI media with different elastic properties. Simple formulae are given for the Fréchet derivatives of the travel time with respect to the elastic parameters and the interface parameters. In the weak anisotropy hypothesis the P-wave travel times are sensitive only to a subset of the orthorhombic parameters: the six P-wave elastic parameters and the three Euler angles defining the orientation of the mirror planes of symmetry. The P-wave travel times are inverted by minimizing in terms of least-squares the misfit between the observed and calculated travel times. The solution is approached using a Singular Value Decomposition (SVD). The stability of the inversion is ensured by making use of suitable a priori information and/or by applying regularization. The technique is applied to two synthetic data sets, simulating simple Vertical Seismic Profile (VSP) experiments. The examples demonstrate the necessity of good 3-D ray coverage when considering complex anisotropic symmetry.