Geometric modeling of underground ferromagnetic pipelines for magnetic dipole reconstruction-based magnetic anomaly detection

To aid the magnetic anomaly detection (MAD) of underground ferromagnetic pipelines, this paper proposes a geometric modeling method based on the magnetic dipole reconstruction method (MDRM). First, the numerical modeling of basic pipe components such as straight sections, bends and elbows, and tee joints are discussed and the relevant mathematical formulations for these components are derived. Next, after analyzing the function of MDRM and various element division strategies, the sectional division and blocked division methods are introduced and applied to the appropriate pipeline components to determine the volume and center coordinates of each element, establishing the general models for the three typical pipeline components considered. The resulting volume and center coordinates of each component are the fundamental parameters for determining the MAD forwarding of underground ferromagnetic pipelines using the MDRM. Finally, based on the combination and transformation of the basic pipeline components considered, the visualized geometric models of typical pipeline layouts including parallel pipelines, pipelines with elbows, and a pipeline with a tee joint are constructed. The results demonstrate the feasibility of the proposed method of geometric modeling for the MDRM, which can be further applied to the finite element modeling of these and other components when analyzing MAD data. Furthermore, the models with output parameters proposed in this paper establish a foundation for the inversion of MAD.