A broad learning approach for magnetic reduction to the pole

Reduction to the pole (RTP) is a fundamental method for interpreting magnetic anomaly data. It faces challenges at low magnetic latitudes and uneven observation surfaces, potentially leading to inaccurate localization of magnetic sources. To address these issues, we develop a novel approach under the machine-learning framework for achieving stable and rapid magnetic RTP in arbitrary regions. First, a single magnetic dipole with random size, position, and magnetization magnitude is used in the forward model to generate samples of the original total magnetic intensity (TMI) anomaly data and the corresponding vertical TMI, which simplifies the establishment of training data. Second, the broad learning system (BLS) is used to establish a mapping relationship between the original and vertical TMI data, as the BLS exhibits a fast network training process due to its concise network structure and strong mapping ability. The combination of the sample generation strategy and BLS allows for rapid network construction and RTP completion. The feasibility of our method is validated by synthetic models and field applications. Synthetic data tests suggest that the BLS approach can be effectively applied to magnetic RTP across various regions, such as the magnetic equator and undulating surfaces. It demonstrates superior accuracy and noise robustness compared to the wavenumber-domain method. Field applications indicate that BLS prediction results facilitate further exploration of mining areas and save over 91% of the time compared with the equivalent source and deep-learning methods. This study is useful for the rapid and accurate localization of magnetic sources and for providing horizontal positional constraints for 3D magnetic inversion.