Electrical anisotropy is a property of the Earth materials that can be studied through electromagnetic geophysical methods, such as magnetotellurics. It consists of the electrical conductivity changing with the orientation and being mathematically characterized by the conductivity tensor. In order to better understand the conductivity tensor and provide more effective tools for quantitatively analyzing the conductivity tensor of anisotropic structures, three graphical representations for symmetric tensors using ellipsoids, Mohr circles and geometric forms are presented. The ellipsoid representation can be applied to indicate the strength of the anisotropy in different directions. The Mohr circle provides a graphic representation of a tensor as a function of the rotation of the coordinate system. For the geometric forms, one-dimensional (1-D), two-dimensional (2-D) and three-dimensional (3-D) sheet models with given parameters (sizes and resistivities of the constituent prisms), the macroscopic anisotropic conductivity may be calculated using the closed-form mathematical formulas. These three graphical representations have different abilities for revealing information on the conductivity tensor. Four synthetic examples involving uniaxial or biaxial anisotropic conductivity structures are examined in the principal axis coordinate system to investigate the advantages and disadvantages of the graphical displays.

中文翻译：

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各向异性介质电导率张量的图形表示和解释

电各向异性是地球材料的一种特性，可以通过电磁地球物理方法（例如大地电磁学）进行研究。它由随方向变化的电导率组成，并由电导率张量进行数学表征。为了更好地理解电导率张量并为定量分析各向异性结构的电导率张量提供更有效的工具，提出了使用椭球、莫尔圆和几何形式的对称张量的三种图形表示。椭球表示可用于指示不同方向的各向异性强度。莫尔圆提供张量作为坐标系旋转的函数的图形表示。对于几何形式，一维（1-D），二维 (2-D) 和三维 (3-D) 片模型具有给定的参数（组成棱柱的尺寸和电阻率），宏观各向异性电导率可以使用封闭形式的数学公式计算。这三种图形表示具有不同的能力来揭示有关电导率张量的信息。在主轴坐标系中检查了四个涉及单轴或双轴各向异性电导率结构的合成示例，以研究图形显示的优缺点。这三种图形表示具有不同的能力来揭示有关电导率张量的信息。在主轴坐标系中检查了四个涉及单轴或双轴各向异性电导率结构的合成示例，以研究图形显示的优缺点。这三种图形表示具有不同的能力来揭示有关电导率张量的信息。在主轴坐标系中检查了四个涉及单轴或双轴各向异性电导率结构的合成示例，以研究图形显示的优缺点。