We present a 2.5-D finite difference (FD) algorithm to simulate the logging-while-drilling (LWD) electromagnetic (EM) measurements with arbitrarily oriented magnetic dipole sources in 2-D anisotropic media. The real 3-D modeling in the spatial domain is converted to a series of independent 2-D equations in the spectral domain by implementing the Fourier transform (FT). By replacing the dipoles with incident fields, the scattered fields are solved directly to avoid the point source singularity as well as improve the convergence of inverse FT (IFT). The efficiency of the IFT is further enhanced with a modified Gauss–Hermite (GHM) quadrature-based numerical integration scheme. Numerical tests demonstrate that the proposed 2.5-D algorithm is fast and accurate in modeling the LWD EM measurements in complex scenarios. Discussions are also made to compare the performance of the proposed methods with 1-D and 3-D algorithms.

中文翻译：

---

2.5维有限差分法在复杂情景测井随钻电磁测量中的应用

我们提出了一种 2.5 维有限差分 (FD) 算法来模拟随钻测井 (LWD) 电磁 (EM) 测量，在二维各向异性介质中使用任意定向的磁偶极子源。通过实施傅里叶变换 (FT)，空间域中的真实 3-D 建模被转换为谱域中的一系列独立的 2-D 方程。通过用入射场代替偶极子，直接求解散射场，避免点源奇点，提高逆傅里叶变换（IFT）的收敛性。改进后的高斯-厄米 (GHM) 基于正交的数值积分方案进一步提高了 IFT 的效率。数值测试表明，所提出的 2.5-D 算法在复杂场景中对随钻随钻测量建模是快速和准确的。