【作者】 李智明；

【导师】 冯锐；

【作者基本信息】 中国地震局地球物理研究所 ， 固体地球物理学， 2003， 硕士

【摘要】 电法勘探是传统的地球物理勘探手段之一，已广泛应用于地质勘察、地下水开采、金属矿产勘探等领域。上世纪八十年代末以来，兼顾电剖面法横向分辨率高和电测深法纵向分辨率高的优点，电阻率层析成像成为继地震波层析成像和电磁波层析成像以后地学CT的重要手段，已初步实现了2维、2.5维数值计算和实际资料处理，并应用于水文、考古学、建筑等领域。目前，3维电阻率层析成像，理论研究和实际应用都处在探索阶段，属于国内外的前沿课题。 本文作者在三维电阻率层析成像的理论研究和实际应用方面开展了全面、细致的研究工作，主要包括： 1 详细推导了采用四面体单元时，有限元法求解三维电阻率正演问题的计算过程，分别给出了异常电位法和总电位法两种方法。探讨了三维电阻率有限元正演程序设计中，可在网格划分时先暂不考虑点电源位置和电阻率分布，计算并磁盘存储各单元D_e,kA^sub(A^sub)^T/1、AI_e,kA^T/比值，对具体电阻率分布和点电源位置，直接从磁盘读取上二比值，从而快速合成总体系数矩阵；分析四面体单元网格形成的总体系数矩阵特点（稀疏、对称、十五对角阵），提出了只存储十五条对角线上元素的按行压缩存储方法，实现了有效存储总体系数矩阵，并节省了大量内存；利用SSORCG算法可高效求解AX=B，并指明该算法中收敛精度和阻尼因子的选取需要考虑具体网格划分和电性分布。正演数值模拟试验在均匀介质、水平二层、垂直断层等简单模型基础上，首次加入三维球体的理论模型，结果表明：采用四面体单元的三维电阻率有限元正演算法正确，异常电位法精度优于总电位法，同时，采用上述方法编制的正演程序正确，可顺利实现复杂的三维正演计箅。 2 分别讨论了三维电阻率反演中层析成像方程、三维观测方式、初始模型建立、偏导数计算、反演方法、探测深度和异常梯分辨率等方面。提出了以观测数据均值为起算模型，将成像区域细分为不重叠的若干深度层后，用三维观测单极—单极法视电阻率投影点落在相应深度层内的观测数据“逐层反演”建立初始模型的方法，表明该法建立的初始模型与真实模型已经很接近，有利于反演的成功。在反演修改上述初始模型时，可利用全部数据反演整个成像区域的“整体反演”进行修改迭代，表明该法修改迭代时，适合做1-2次数迭代修改，并可避免反演修改过度现象。提出了三维电阻率反演时，确定阻尼最小二乘法中阻尼因子的算法及加速方法，保证了快速进行反演计算。针对三维电阻率反演问题的多解性，明确引入了非负约束等约束条件。大量反演数值模拟试验表明：“逐层反演”建立初始模型、“整体反演”进行反演修改迭代，以及引入适当约束条件，三者结合能得到较好二维成像结果;二维观测中单极一单极法时，深度系数取0.8是合适的;异常体分辨率与异常体分布、电性差异、偏导数计算精度和约束条件等因素有关，尚待进一步研究。 3将上述二维电阻率层析成像方法成功用于活断层、考古探测，提供了精细的二维电阻率分布图像和地质解释。表明:三维电阻率层析成像有效揭示了断层在浅部区域的空间延伸，适合‘维电阻率层析成像后，对异常地段的精细二维研究;可初步判明考古探测中理藏的可能空间位置，为挖掘「作提供参考。上述实际应用为三维电阻率层析成像技术的实际应用提供了可靠性检验和宝贵经验。 此外，针对石油部门注水驱汕过程，本文作者尝试提出了“线源二维目标层电阻率异常反演气介绍了观测系统、偏导数计算方法，提出了无需关注初始模型，直接利用注水前后的电位异常数据来反演注水前后电阻率异常方分布，指示可能的剩余油气分布方位。初步应用于石油开发应用，表明该法用于监测剩余油气分布是可行的，同时该项也指明了后续_!;作的研究重点。 作者在研究生期间参加过北京奥运村地区活断层项目中13条剖面、总长度约14km的二维电阻率层析成像探测的野外施_l二，数据处理和报告编写，以及山东淄博地区张店一仁河断裂、新店地区二维电阻率层析成像探测任务。这些实践活动都帮助加深了对电阻率层析成像技术的理解，成为开展二维电阻率层析成像研究的直接动力。更多还原

【Abstract】 Electrical prospecting is one of traditional geophysical exploration methods. It has been widely applied in the fields of geological examination, ground water development, mining exploration, et al. From 1980s, having higher horizontal resolution of electrical profiling and higher vertical resolution of electrical sounding, resistivity tomography has become an important approach of geoscience CT that have had seismic wave tomography and electromagnetic wave tomography. It has been carried out in 2-D and 2.5-D numerical calculation and disposal of practical materials, and applied in hydrology, archaeology, architectonics, et al. Now, 3-D resistivity tomography is still an advanced problem in the world, and it is also under development, whether in theoretical research or in practical application.In this paper, author developed detailed and comprehensive system work in 3-D resistivity tomography theoretical research and practical application. These works included:1. Author detailedly deduced the calculation process of 3-D resistivity forward with finite element method when adopting tetrahedron element griddings, gave two calculation methods, anomalous potential method and total potential method, then discussed in the programming of 3-D resistivity finite element forward. When the location of point current is altered and the resistivity distribution is changed, the location and distribution could not be considered during constructing the griddings, calculated and storedtwo ratios of each tetrahedron element, DekAsub(Asub)T/I, AIe,kAT/2, in disk files. As soon asresistivity distribution and location of point power was concentrated, those ratios were read from disk files directly, then total coefficient matrix was assembled rapidly with element coefficient matrixes. A new compressible store method is brought out in which elements locating fifty diagonals in total coefficient matrix are only stroed, which could be store total coefficient matrix effectively, and save a lot of memories. Linear equation, AX=B, was resolved by SSORCG algorithm and some examples demonstrated that in this algorithm, griddings scheme and electrical property distribution need be considered. Besides numeric simulation of homogeneous medium modal, two horizontal layers modal, and vertical fault modal, author firstly added in 3-D sphere model, the result indicated that 3-D resistivity forward with tetrahedron elements is right, that abnormal potential method is prior to total potential method and that Adopting above methods to build forward programming is right and effective to calculate complex 3-D forward problem.2. Author discussed resistivity tomography equation, 3-D resistivity measurement, establishment of initial model, calculation of partial derivative and inversion method, detected depth, and resolution of abnormal bodies in order. A effctive to constructure initial modal was developed, in which step-layered inversion was employed. The results indicated that the initial model established with this method was very close to the true model, and this method would lead to inversing successfully. When modifying an initial model with step-layered inverion method, author used integer inversion in whch all data were used to inverse whole imageing region, and some modelling indicated that this way was proper to deal with one or two times iteratation and it would avoid over-inversion. Author also put forward the arithmetics to calculate and accelerate dump factor in dumping least squares method. To multi-solution character in 3-D resistivity inversion problem, author definitely inducted constraint condition ,such as non-negative condition. A lot of theoretical inversion simulation showed that better inversion result can be obtained by combining step-layered inversion method to establish initial model and integral inversion method to modify model, that the depth-coefficient, 0.8, is appropriate during calculating the projection depth of apparent resistivity measured with 3-D measurement under pole-pole configuration and that更多还原