Triaxial induction logging tools have been widely applied to formation characterization due to their sensitivity to electric anisotropy. To model triaxial induction logs in multilayered general anisotropic formations, where the anisotropy can be arbitrary, an analytical method is applied to compute the tool responses. For the analytical method, Maxwell’s equations in the spectral domain are written into a compact first-order differential equation. The equation is solved to obtain the spectral-domain fields, which are transformed to the spatial domain through the inverse Fourier transform. The singular issue for the tool located in highly deviated wells is handled by subtracting the singular term in the spectral domain. The singularity treatment makes the integrands in the inverse Fourier transform decay faster, thus making the infinite integration computation faster. Formations with isotropic, transversely isotropic, biaxially anisotropic, and general anisotropic conductivity are modeled and compared to investigate the effects of anisotropy on the tool responses. For a tool in a general anisotropic formation, all of the $\mathbf{H}$ components are nonzero. For a tool in a vertical well in transversely isotropic and biaxially anisotropic formations, only the diagonal components of $\mathbf{H}$ are nonzero. For a tool located in a deviated well, the effects of tool deviation and electric anisotropy are coupled. The diagonal components are more sensitive to the electric anisotropy than the off-diagonal components, and the off-diagonal ones can clearly indicate bed boundaries.

中文翻译：

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多层各向异性地层中三轴感应测井响应的建模

三轴感应测井仪因其对电各向异性的敏感性而被广泛应用于地层表征。为了模拟多层一般各向异性地层中的三轴感应测井，其中各向异性可以是任意的，分析方法被应用于计算工具响应。对于解析方法，将谱域中的麦克斯韦方程组写成一个紧凑的一阶微分方程。求解该方程以获得谱域场，通过逆傅立叶变换将其变换到空间域。位于大斜度井中的工具的奇异问题是通过减去谱域中的奇异项来处理的。奇点处理使得逆傅里叶变换中的被积函数衰减得更快，从而使无限积分计算更快。对具有各向同性、横向各向同性、双轴各向异性和一般各向异性电导率的地层进行建模和比较，以研究各向异性对工具响应的影响。对于一般各向异性地层中的工具，所有的$\mathbf{H}$组件非零。对于在横向各向同性和双轴各向异性地层中的垂直井中的工具，只有$\mathbf{H}$非零。对于位于斜井中的工具，工具斜度和电各向异性的影响是耦合的。对角线分量比非对角线分量对电各向异性更敏感，并且非对角线分量可以清楚地指示层边界。