An efficient algorithm for the response of gyrotropic-like anisotropic media in arbitrary deviated Wells

To expedite forward simulation studies, this paper proposes a universal analytical algorithm for calculating gyrotropic-like anisotropic formation models. the Maxwell equation system underwent a 2D Fourier transform, yielding a set of ordinary differential equations featuring the system matrix, field vector, and source vector. The response in the medium model is obtained by solving the differential equation. We introduce the reflection and propagation matrices to describe electromagnetic wave propagation at the stratigraphic interfaces, and obtain the frequency domain response of electromagnetic waves at each layer. Finally, a two-dimensional inverse Fourier transform was applied to translate the frequency domain responses into the spatial domain. The accuracy of the algorithm was verified by comparing the calculated results with the numerical simulation algorithm results. Moreover, the eigenvalues of the system matrix are uniquely defined and are associated with factors such as formation parameters and anisotropy. The characteristic values of various types of anisotropic formation system matrix are analyzed, which not only contributes to extracting formation information but also provides a basis for geological interpretation and oil and gas exploration.