三维大地电磁正演快速算法研究

发布时间：2018-06-02 08:03

本文选题：大地电磁 + 频率自适应矢量有限元法　；参考：《吉林大学》2017年硕士论文

【摘要】：大地电磁测深法(MT)是一种频率域电磁勘探方法,它以天然交变电磁波为场源对地下介质进行研究;由于不需要人工源,因此其具有野外工作简单、成本低、受野外地质条件约束较小等特点。此外,这种方法还有不会被高阻临层屏蔽和对低阻体响应敏感等优点,使其在区域性地质调查、矿产普查、深部地质构造研究等领域得到广泛的应用。进行大地电磁正演数值模拟,能让我们对各种不同电性结构所产生电磁场的规律有更深刻的认识。本文应用频率自适应矢量有限元法实现了大地电磁三维正演数值模拟并使用拟线性积分方程法进行了特定模型电场值的快速计算。首先,本文从MAXWELL方程组出发,根据三维大地电磁所满足的边值条件,利用Galerkin法推导了与三维大地电磁边值问题等价的变分方程。然后采用正六面体单元对计算区域进行剖分,并使用矢量插值基函数进行单元分析。最后把各个单元相加,形成巨大而稀疏的系数矩阵;进而将矩阵储存并求解。接着,我们发现当对计算区域网格进行正六面体剖分时,在电性剧烈变化的区域,有可能因为网格剖分的不够细致,从而导致六面体单元中的场值无法通过其十二条矢量边的插值函数准确表达,造成误差。另外,由于大地电磁场的边界条件在无穷远处才能得到满足;所以不恰当的网格剖分策略可能造成数值模拟计算结果误差过大。进而,本文又研究了不同频率下误差产生的原因及规律。根据上述的误差分析,本文提出了基于正六面体单元矢量有限元法网格划分的基本原则,并据此原则对正演过程进行改良,提出了频率自适应的想法,随着频率的变化不断调整剖分网格的方式;在保证计算精度的情况下大幅提升了计算速度。最后,对一系列地质模型进行了正演模拟和分析,以及通过利用格林函数的空间对称性和互换定理,压缩了格林系数的计算量,加快系数矩阵的生成速度,实现快速拟线性近似方法,并使用拟线性积分方程法进行了特定模型电场值的快速计算;并提出了一些不足以及对日后工作的建议。
[Abstract]:The magnetotelluric sounding method (MTM) is a frequency-domain electromagnetic exploration method, which uses natural alternating electromagnetic waves as a field source to study underground media. It is limited by field geological conditions and so on. In addition, this method has the advantages of not being shielded by high resistivity impending layer and being sensitive to the response of low resistivity bodies, which makes it widely used in regional geological survey, mineral survey, deep geological structure research and other fields. The numerical simulation of magnetotelluric forward modeling can give us a better understanding of the law of electromagnetic field generated by various electrical structures. In this paper, the frequency adaptive vector finite element method is used to realize the 3-D forward numerical simulation of magnetotelluric and the fast calculation of the electric field value of the specific model is carried out by using the quasilinear integral equation method. Firstly, based on the MAXWELL equations and the boundary conditions satisfied by 3D magnetotelluric, the variational equations equivalent to 3D magnetotelluric boundary value problems are derived by using Galerkin method. Then the normal hexahedron element is used to divide the calculation area and the vector interpolation basis function is used to analyze the element. Finally, the various elements are added together to form a large and sparse coefficient matrix, and then the matrix is stored and solved. Then, we find that when the computing area mesh is divided into hexahedron, it is possible that the grid is not detailed enough in the area where the electrical property changes dramatically. As a result, the field value in hexahedron element can not be accurately expressed by the interpolation function of its twelve vector edges, resulting in errors. In addition, the boundary conditions of the magnetotelluric field can only be satisfied at infinity, so the improper mesh generation strategy may cause the error of the numerical simulation results to be too large. Furthermore, the causes and rules of errors at different frequencies are studied. Based on the above error analysis, this paper puts forward the basic principle of mesh generation based on the vector finite element method of hexahedron element, and improves the forward modeling process according to the principle, and puts forward the idea of frequency adaptation. With the change of frequency, the method of mesh division is adjusted continuously, and the calculation speed is greatly improved under the condition of ensuring the accuracy of calculation. Finally, the forward modeling and analysis of a series of geological models are carried out, and by using the spatial symmetry of Green's function and the exchange theorem, the calculation of Green's coefficient is compressed, and the generation speed of coefficient matrix is accelerated. The fast quasilinear approximate method is realized, and the fast calculation of electric field value of a specific model is carried out by using the quasilinear integral equation method, and some shortcomings and suggestions for future work are put forward.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P631.325

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