A fast magnetic forward modeling for high susceptibility considering demagnetization

Strongly magnetic bodies with complex shapes pose a challenge in magnetic exploration due to the significant demagnetization effect in an external magnetic field during the magnetization process. Analytical formulas are not directly applicable to solving the magnetic field generated. We propose a fast-forward algorithm that considers the demagnetization effect to address this. The algorithm uses an improved convolution-based method to improve computational efficiency by transforming convolution operation in the spatial domain into dot product operation in the frequency domain. Moreover, the relaxation iteration algorithm is introduced to ensure the convergence of the iterative solution of the integral equation. Specifically, the strongly magnetic body is first divided into cubic subunits, and the mutual magnetization magnetic field between them is calculated. Then, each subunit's final effective magnetization intensity is iteratively calculated using the relaxation algorithm, and the magnetic field generated by the strongly magnetic body at the measurement point is accumulated. We verified the stability and accuracy of the algorithm using a theoretical spherical model. Our algorithm is significant for accurately exploring minerals, underground pipelines, and unexploded ordnance (UXO).