Iterative magnetic forward modeling for high susceptibility based on integral equation and Gauss-fast Fourier transform

Abstract

Self-demagnetization due to strongly magnetic bodies can seriously affect the interpretation of magnetic anomalies. Conventional numerical methods often neglect the self-demagnetization effects and limit their use to low susceptibilities ([Formula: see text]). We have developed a novel iterative method based on the integral equation and the Gauss-fast Fourier transform (FFT) technique for calculating the magnetic field from finite bodies of high magnetic susceptibility and arbitrary shapes. The method uses a segmented model consisting of prismatic voxels to approximate a complex target region. In each voxel, the magnetization is assumed to be constant, so that the integral equation in the spatial domain can reduce to a simple form with lots of merit in numerical calculation after the 2D Fourier transform. Moreover, a contraction operator is derived to ensure the convergence of the iterative calculation, and the Gauss-FFT technique is applied to reduce numerical errors due to edge effects. Our modeling results indicate that this new iterative scheme performs well in a wide range of magnetic susceptibilities (1–1000 SI). For lower susceptibilities ([Formula: see text]), the iterative algorithm converges rapidly and indicates very good correlation with the analytical solutions. At higher susceptibilities ([Formula: see text]), our method still performs well, but the numerical accuracy improves with a relatively slow speed. In the extreme case ([Formula: see text]), an acceptable result is also obtained after sufficient iterative computation. A further improvement in the numerical precision can be achieved by increasing the number of prismatic voxels, but at the same time, the computational time increases linearly with the size of the voxels.