Integral-Equation Modeling of Magnetic Field in Anisotropic Media: Effects of Strong Demagnetization and Remanence

Summary For magnetic forward modeling in anisotropic media involving strong self-demagnetization and remanent magnetization, an iterative integral-equation solver based on quadratic shape-function interpolation is developed. The proposed method employs a two-dimensional Fourier transform to reduce the three-dimensional magnetic potential integral equation to a one-dimensional vertical form, which is then discretized using quadratic shape functions. By extending the isotropic iterative operator to a tensor form, a stable iterative scheme suitable for strongly magnetic anisotropic media is constructed. The accuracy of the algorithm is verified using anisotropic ellipsoid models with analytical solutions and further evaluated by finite-element benchmarks. In addition, a comparison between linear and quadratic vertical interpolation schemes shows that the quadratic scheme provides a better balance among numerical accuracy, computational efficiency, and memory usage. Sensitivity analyses and convergence tests indicate that the maximum principal susceptibility is the dominant factor controlling iterative convergence; as it increases, the number of iterations rises, whereas the numerical error remains stable. Euler-angle rotations systematically modify the effective susceptibility tensor and significantly affect the morphology of magnetic anomalies. Remanent magnetization acts as a fixed source term that changes the amplitude and spatial distribution of the magnetic response but does not affect the number of iterations in the tested cases. Computational tests demonstrate that the proposed method requires less runtime and memory than finite-element modeling under the same target discretization conditions, and OpenMP parallel tests indicate that the algorithm exhibits good parallel performance. Application to a complex salt-dome model further confirms that susceptibility anisotropy and Euler-angle rotations can substantially alter magnetic anomaly patterns for irregular geological bodies. Overall, the proposed method provides a reliable and efficient tool for high-accuracy magnetic forward modeling of strongly magnetic anisotropic media under coupled self-demagnetization and remanent magnetization conditions.