Spatiotemporal Variation Characteristics of Magnetic Anomaly Field Induced by a Submerged Vessel

High-precision magnetic anomaly field modeling is crucial for the development of magnetic detection and stealth technologies of submerged vessels. This paper aims to reveal how depth and speed influence the magnetic anomaly field of submerged vessels, thus providing a theoretical foundation for magnetic stealth and detection technologies. A single-shell vessel model without appendages was developed to simplify magnetic characteristic analysis. The finite element method, based on Gauss's law for magnetism and Maxwell-Ampere's law, was employed to compute the spatial characteristics of the magnetic anomaly field. Moreover, the stationary solution and parametric sweep analysis were integrated to simulate the temporal characteristics of the magnetic anomaly field as the vessel sailed at different depths and speeds. The results indicate that the magnetic anomaly field intensity peaks directly above the vessel and diminishes with increasing detection distance. The maximum absolute values of the magnetic anomaly vector field are inversely proportional to depth, with the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{x}$</tex> -component being dominant, followed by the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$z$</tex> - and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{y}$</tex> -components. Additionally, the depth most impacts the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$z$</tex> -component and least the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{x}$</tex> -component. As the vessel's speed increases, the traversal time shortens and waveform width narrows, but the intensity remains largely unaffected. In conclusion, this research offers essential theoretical support for the magnetic detection and stealth of submerged vessels. Future research should take into account more complex vessel models and real-experiment data.