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可控源音频大地电磁法（CSAMT）是一种在大地电磁法和音频大地电磁法基础上发展而来的地球物理勘探方法，采用人工可控的发射场源，使其具有噪比高、抗干扰能力强等诸多优点，在金属矿产资源勘探、海洋油气勘探和地下水寻找等领域有着广泛的应用。随着实际生产中所需勘探的地质体越加复杂，一维、二维的资料处理和解析已经满足不了生产需求，因此有必要进行三维的可控源电磁法正反演研究。正演数值模拟是反演的基础，因此本论文主要开展了可控源音频大地电磁三维矢量有限元正演模拟及2.5D和3D可控源音频大地电磁法正演结果的对比研究。首先，利用傅里叶变换对麦克斯韦方程组进行波数域的转换，推导了电场磁场相互耦合的带场源项的微分方程，并进行加权余量变分处理，然后通过节点有限单元法和伪Delta等效场源得到线性方程组，求解方程组并进行反变换得到2.5维的电磁响应。与解析解进行对比验证后，对不同地质模型的2.5维可控源电磁响应进行详细分析，发现其视电阻率和相位对不同地质模型所具有的探测能力有所不同。其次在进行三维可控源电磁法正演中，从由Maxwell方程推导出的二次电场的双旋度方程出发，可以减弱场源的奇异性和避免对电流密度求旋度，简化求解过程；选用矢量有限单元法来求解，使得散度条件自动满足；对研究区域进行非均匀网格的六面体剖分和线性插值，详细进行了单元分析；分析了大型稀疏线性方程组的不同存储方式，并对求解方程组的直接法和迭代法进行对比分析，发现迭代法所需内存更小、速度更快。实现程序编写并与有限差分法进行三维模型的验证分析，验证算法的正确性。而后对不同地质模型的三维电磁响应进行详细分析，并与2.5维可控源电磁响应结果进行对比，得到一些结论：对应不同阻抗的视电阻率和相位对地质体的反映能力有所不同；2.5D模拟效果与3D的差异较大，主要集中在电性变化较为剧烈的位置；3D正演对异常体边界分辨能力较2.5D的要高，2.5D正演的相位响应效果较3D的要好；频率不同时，2.5D的视电阻率和相位响应效果与3D之间的差异有所不同，且对不同的地质模型，二者的视电阻率误差和相位误差也有所不同。

Controlled source audio magnetotelluric (CSAMT) is a geophysical exploration method developed on the basis of magnetotelluric method and audio-frequency magnetotelluric method. It has many advantages, such as high signal-to-noise ratio and strong anti-interference ability, by using artificially controllable emitters. Therefore, it has been widely used in the fields of metal mineral resources prospecting, marine oil and gas and groundwater investigation. With more complex geological objects to be explored in production, one-dimensional and two-dimensional data processing and analysis cannot meet the production needs, so it is necessary to carry out three-dimensional forward and inverse modeling of CSAMT. Forward modeling is the basis of inversion, so this paper mainly achieves three-dimensional forward modeling of CSAMT by vector finite element, and compares with 2.5-dimensional forward modeling of CSAMT realized in this paper, and draws conclusions.Firstly, Maxwell's equations in frequency domain are converted to the wavenumber domain by Fourier transform, and the differential equations with source terms, coupling electric field and magnetic field, are deduced. Then, the linear equations are obtained by nodal finite element method and pseudo-delta equivalent source. The equations are solved and the 2.5-dimensional electromagnetic response is obtained by inverse transformation. After comparing with the analytical solution, the 2.5-D CSAMT response of different geological models is analyzed in detail, and it is found that the apparent resistivity and phase have different detection capabilities for different geological models. Then, in the forward modeling of three-dimensional CSAMT, based on the double curl equation of the secondary electric field derived from Maxwell equation, the singularity of the field source and the curl of the current density can be avoided, and the derivation can be simplified. The vector finite element method is used to solve the problem so that the divergence condition can be satisfied automatically. The hexahedron partition and linear interpolation of non-uniform meshes are carried out in the study area, and the element analysis is accomplished in detail. The different storage methods of large sparse linear equations set are analyzed, and the direct method and iteration method for solving the equations are compared. It is found that the iteration method needs less memory and solves the equations faster. The method is programmed by matlab and verified by finite difference method in three-dimensional model simulation. After verifying the validity of the algorithm, the three-dimensional electromagnetic responses of different geological models are analyzed in detail, and the results are compared with those of 2.5-dimensional CSAMT. Some conclusions are drawn: (1) The apparent resistivity and phase corresponding to different impedance have different detectiviti to geological bodies. (2) The results of 2.5D simulation differ greatly from those of 3D simulation, mainly in the places where the electrical properties change dramatically. (3) The 3.D forward modeling has higher resolution to the boundary of anomalous body than 2.5D. (4) At different frequencies, the differences of apparent resistivities and phases of 2.5D forward modeling differ from that of 3D, and the apparent resistivity and the phase errors of different geological models are also different.