【作者】 刘小军；

【导师】 王家林；

【作者基本信息】 同济大学 ， 固体地球物理学， 2007， 博士

【摘要】 大地电磁测深法(MT)是在地面上观测具有区域性乃至全球性分布特征的天然交变电磁场来研究地下岩层的电学性质及其分布特征的一种探测方法。它通过研究大地对天然电磁场的频率响应，获得地下不同深度介质电阻率分布的信息。由于该方法不需要人工建场、成本低、勘探深度大等优点，已广泛应用于研究地壳和上地幔地质构造，同时也用来进行油气勘查、地热勘探及地震预报等研究工作。随着MT的广泛应用和对其理论研究的深入，许多问题也显现出来，特别是在高维、高精度大地电磁数据反演方法的研究方面进展较缓慢。本论文以中科院知识创新工程重大项目“环渤海(湾)地区前新生代海相油气资源研究”中的“环渤海(湾)地区前新生代残留盆地分布的综合地质地球物理研究”课题和中国石化西部新区勘探指挥部的科研项目“准南山前带非地震成像技术研究”为依托，分析了当前大地电磁数据反演的发展现状；鉴于传统的反演方法大都是基于最大平滑理论基础上，反演得出的地电图像都是渐变的，不能准确反映出电性突变时分界面的具体位置。针对这一问题，在前人工作的基础上，提出了大地电磁数据聚焦反演成像方法技术。根据聚焦反演方法固有的特点和需要，研究了基于计算二次场响应的MT模拟方法，构建了新的反演目标函数并对解反演目标函数的方法进行了优化，较好地实现了本次研究的目的。论文的主要内容与成果如下：(1)当前二维大地电磁有限元正演模拟方法都是直接计算平行于走向的总场值，这种计算思路受网格密度的影响较大，而且在求取低频段的电磁场响应时解的精度偏低。针对这一问题，引入基于计算二次场响应的模拟方法。将非均匀地电结构中传播的大地电磁场分解为一次(电或磁)场与二次场之和，其中一次场为无异常体时的场，二次场为异常体产生的场。在使用有限元法解偏微分方程时，利用二次场偏微分方程与总场偏微分方程的相似性，直接引用总场法计算中的系数矩阵作为二次场方程的合成矩阵。与总场偏微分方程相比较，二次场方程只是在右端多了一个源项积分，因此总场法的有限元系数矩阵可直接用于求二次场的方程中。这种模拟方法受网格密度影响较低，而且较好地解决了总场法中低频场精度不高的缺点。根据上述原理所编制的二次场有限元法MT正演模拟软件，对几个典型模型进行了试算，并与传统总场模拟法进行了比较分析。结果表明直接计算二次场的结果精度更高、更接近真实解，这一方法的提出对提高大地电磁反演精度具有理论和实践意义。(2)当前MT反演方法在构建目标函数时大都选择基于最大平滑稳定泛函作为模型目标函数，采用这种思路反演出的地电图像都是平滑的、渐变的，不能准确反映岩体电性突变时分界面的具体位置，这给后期的地质解释带来了一定的困难。本文分析了Oleg Portniaguine等人(1999)年提出的聚焦反演成像法，此方法是建立在一种全新的稳定器(如最小梯度支撑泛函等)的基础上，并结合惩罚泛函，将其作为反演模型目标函数。论文中简要说明了当前地球物理反演中几种常用的模型目标函数之后，根据聚焦反演成像方法的基本理论，并在大地电磁反演目标函数中引入一个新的稳定泛函一最小支撑泛函，代替传统最小构造或最大平滑准则下的模型目标函数。在构建新的目标函数后，编写了相应的程序并做了模型试验，反演出的结果比常规最大平滑类反演方法得到的地电图像更聚焦、清晰，对电性界面确定的更加准确。(3)针对二维反演迭代过程中计算观测数据对于参数的灵敏度矩阵占用大量CPU时间的问题，提出利用互换定理、采用有限单元法计算灵敏度矩阵的思路。基本原理是根据源点与接收点可以互换的原理，将源点放到MT的测点处，这样做一次正演计算就可以求得测点上主场对研究区所有单元的偏导数，辅助场偏导数的计算方法也可采取相同的原理。采用这种思路，将计算灵敏度矩阵总共所需要的正演次数减少到了测点数，与差分法相比计算速度有很大提高。在第一次迭代后，引入Broyden公式更新灵敏度矩阵，大大减少了迭代周期。(4)引入再加权的正则化思想，采用共轭梯度法求解最优化问题。在解目标函数极小值问题时，引入再加权正则化的思想，基本思路是在共轭梯度法的迭代过程中，根据目标的收敛情况更新正则化因子。这样有效地解决了迭代时目标函数发散的问题，保证了反演的稳定性并提高了目标函数的收敛速度。(5)通过数值模型和实测资料的试验，证明了本论文研究算法的有效性和实用价值。应用编写的程序进行了典型模型的试算，并与传统反演算法的计算结果进行了对比分析；对徐闻地区多条实测MT资料进行聚焦反演成像处理，并与地震资料进行了对比分析，最后与综合地质解释进行了比较，结果表明了聚焦反演的准确性和实用性。更多还原

【Abstract】 The magetotelluric sounding is an excellent geophysical tool by measuring thesurface electromagnetic response of earth and analyzing the character ofelectromagnetic field to study the rock electricity and character of conformation. Theprinciple of MT is deducing the geoelectrical structures by analysing theelectromagnetic frequency response of earth. MT is used to study the structuralfeature of earth crust and upper mantle for the excellence that needn’t the artificialelectromagnetic field and can get the deep information of earth. However, with thewide practical application and in-depth theory research, lots of new problems arepresented and need to be solved. Sponsored by CAS and Sinopec, focusing inversionimages method is presented and advantage of the method is proved. The maincontents and achievements of the thesis are following:(1) An efficient method named secondary finite element method (SFEM) ispresented to two-dimensional magnetotelluric numerical modeling, which solves forsecondary variations in the field. During deducing the rationle of the new procedurewe divide total field into primary and secondary field. Then we just need to solve thesecondary field equations for the primary field can get easily. The equations of thesecondary field are solved effortless by finite element method when the boundaryconditions are simple. The effect of resolution is analysed when we deal with theresponse of synthetic model by the secondary field and compare with the results usingtotal field FEM.(2) Usually a maximum smoothness stabilizing functional is used to stabilize theinversion process. The obtained solution is a smooth image by the traditionalstabilizer, which in many practical situations does not describe the examined objectproperly. During narrating the procedure of the approach, we analyse the character ofseveral traditional model object functions firstly, then introduce a new stabilizingfunctional named minimum support stabilizer and the new parametric functional ispresented. The simulated results show the program is right and this approach helps togenerate much more "focused" and resolved images of blocky geoelectrical structures than conventional MT inversion.(3) To speed up the calculation of the sensitivity matrix for 2-D magnetotelluricinversion using finite elements, the principle of electromagnetic reciprocity is applied.The governing relationship for the Jacobians of the field along strike is obtained bydifferentiating the Helmholtz equation with respect to the conductivity of each regionin the finite element mesh. According to the principle of electromagnetic reciprocity,the roles of sources and receivers are interchangeable. Utilizing reciprocity, the fieldvalues obtained from the original forward problem and for new unit sources imposedat the receivers are then utilized in the calculation of the Jacobian by simplemultiplication and summation with finite-element terms at each rectangle in the mesh.Reciprocity decreases the computational expense of Jacobians to the order of thenumber of stations of interest. After the first inversion, the sensitivities matrix isupdated by the Broyden updating formula, which saves the computational timegreatly.(4) The approach of Reweighted Conjugate Gradient is based on regularizationtheory and adaptive regularized factor. Conjugate Gradient Algorithm is utilized tosearch for the minimum of the parametric functional. The optimal regularizationparameter is updated on subsequent iteration if the misfit does not decrease fastenough. This procedure insures the convergence of the inversion and enhances thespeed of inversion calculation.(5) The simulated results of several synthetic data and imaging of field data inXuwen area are presented by focusing inversion, which are higher resolution thanusing conventional inversion method of MT data. All of these indicate the inversionapproach can describe the blocks structures correctly.更多还原