Electromagnetic Logging Response in Multilayered Formation With Arbitrary Uniaxially Electrical Anisotropy

Transversely isotropic (TI) formation is the most popular anisotropic electrical model for computing the electromagnetic (EM) field in multilayered media. However, the TI formation considers only electric parameters such as resistivity along the horizontal and vertical directions, which are not always available in real-life situations. The realistic electric parameter distribution mainly depends on the sedimentary formation environment and could be in arbitrary directions. This article developed a fast-forward algorithm used to calculate the EM field in multilayered media with arbitrary uniaxially electrical anisotropy. Formation resistivity, anisotropic dip, and anisotropic azimuth are adopted to characterize the arbitrary uniaxial anisotropic resistivity media. Half-space Fresnel coefficients are defined and used to analyze the EM reflection and transmission characteristics between different anisotropic media. Generalized reflection and transmission matrices are derived to express the EM field in arbitrary layers. To validate the proposed algorithm, we modeled the traditional logging while drilling (LWD) and triaxial induction tool responses under different conditions. The numerical results agree with the finite element results, demonstrating the feasibility, robustness, and stability of the algorithm.