一种改进的阻抗张量分解方法及其应用

【作者】 李伟；

【导师】 严家斌；

【作者基本信息】 中南大学 ， 地球探测与信息技术， 2010， 硕士

【摘要】 由于近地表电性结构的非均匀性,会导致大地电磁阻抗张量产生畸变,为了描述地质体真实的电性结构特征,往往对大地电磁阻抗张量数据进行畸变分解,如果不对畸变的阻抗张量数据进行畸变消除,将会获得不正确的视电阻率和相位,影响后续的数据处理与解释。本文从大地电磁场的畸变效应入手,分析了三维／一维与三维／二维电性结构模型下阻抗张量畸变的特征,讨论了畸变分解理论的数学和物理含义,总结了常用的大地电磁阻抗张量分解方法,通过对GB分解方法实现的探讨及分析现有方法的不足,提出了一种改进的阻抗张量分解方法,并推导了该方法实现的计算公式,给出了方法实现的具体流程。在计算过程中首先采用广义逆矩阵算法进行求解,并比较了牛顿法与广义逆算法的性能。然后模型验证表明SWIFT旋转在存在畸变干扰时并不能有效地估计阻抗张量及构造的主轴方向及主阻抗值,但可作为本方法的初值估计。利用依格尔斯特征态分析对各向异性因子进行了初值估计。最后对改进的算法进行了模型验证与比较分析并对实测数据进行了处理。编制的程序代码是在数值计算软件Matlab下面实现的,简洁明了。最后将此方法应用到实际的高频与低频大地电磁资料处理中,获得了反映地下真实电性结构特征的区域阻抗张量等参数,对所求得的结果进行了对比分析,得到比较满意的结果。通过本文提出的方法获得的阻抗张量分解各种参数,可以定量分析各种畸变参数对区域阻抗张量产生的变化。若表征各向异性的畸变参数的变化,会使得走向主轴方向和倾向主轴方向发生被压缩或是被拉伸的变化；表征扭转和剪切的畸变参数正负值的变化,会使得阻抗张量发生顺时针或是逆时针的旋转。更多还原

【Abstract】 For the impedance tensor distortion, resulted by horizontal galvanic heterogeneity near surface, it is necessary to decompose the distorted impedance tensor, in order to describe true electrical structural feature. If the distortion of the impedance data is not eliminated, the calculated apparent resistivity and phase may be wrong, which effluence on the result of data processing and interpretation.In this thesis, based on the distorted impedance tensor feature of 3D/1D or 3D/2D model, we discuss several distortion decomposition methods. By analyzing the process of GB decomposition method, an improved method is introduced, using the generalized inverse matrix algorithm to calculate regional impedance from the data in which the distortions have been eliminated. A computer program to carry out this method is written with Matlab, succinct and clear. By forwardly calculating a theoretical model under the effluence of the distortion factors, we detect the error of the generalized inverse matrix algorithm and prove it to be effective. Finally, the improved method is applied into the calculation of regional impedance from some given magnetotelluric data, which proved to be practical and effective.The method introduced in this thesis can be used to calculate the distortion factors. Therefore, the quantitative relation between the distortion factors and regional impedance can be studied. Gain enlarges or reduces the amplitude of tensor impedance. Principal axis direction of Strike is compressed and perpendicular axis is stretched if anisotropic parameter is a positive value. Oppositely, perpendicular axis is compressed, and Principal axis direction of Strike is stretched. Tensor impedance rotates in clockwise direction under positive twist parameter. Negative shear parameter makes tensor impedance rotating in anti-clockwise direction.更多还原