## 5 Results and Discussion  
This study demonstrated the advantages of employing an aluminum-alloy USV for shipborne magnetic surveys, including a significant reduction in magnetic interference compared to conventional ferromagnetic vessels. However, despite the use of a paramagnetic hull, the presence of residual ferromagnetic components, such as motors and other accessories, necessitates appropriate magnetic correction methods. The error histograms and NRMSE values clearly show that comprehensive correction accounting for both attitude and magnetization (i.e., using Equations (3) and (4)) yields significantly improved outcomes compared to attitude correction alone, even with the paramagnetic platform (Figures 5 and 6). In particular, the histograms of misfit against the IGRF model [30] illustrate the improved performance of Equation (3) [25] compared to the other methods (Figure 6). A key difference lies in their mathematical structure and optimization approach. Equation (2) [24] exhibited numerical instability, potentially due to its direct dependence on the noise containing observed magnetic field (H\({}_{\text{obs}}\)) and possible exclusion of non-orthogonality corrections. Equation (4) [26], structurally similar to Equation (2), integrates a non-orthogonality correction matrix (P) into Equation (2). However, this method only considers the principal components (xx, yy, zz) of the magnetic susceptibility tensor, neglecting the off-diagonal terms (xy, xz, yz). In contrast, Equation (3) [25] utilizes all nine components of the susceptibility tensor, providing a comprehensive model for induced magnetization described by the complete tensor. Furthermore, although Equation (3) does not explicitly combine the non-orthogonality correction matrix, its mathematical structure offers an advantage. From this perspective, the nine susceptibility tensor components are linear coefficients relating the induced field to the ambient field components. Consequently, solving for these coefficients inherently corrects not only for the nine components of the vessel's susceptibility but may also automatically compensate for other noise sources exhibiting linear behavior with respect to the ambient field, potentially including non-orthogonality effects or linear drifts. This comprehensive linear correction likely contributes significantly to its improved performance compared to the other methods. Our comparative analysis demonstrates that Equation (3) [25], which utilizes all nine components of the susceptibility tensor and performs comprehensive linear correction, is the most robust method for simultaneously compensating for vessel attitude and induced magnetization. These findings suggest that even when using low-magnetic platforms, precise correction for both attitude and residual magnetization is essential to obtain accurate vector magnetic data. To quantify the benefit of using this optimal correction method on the paramagnetic platform, we compared our USV results with reference data from the ferromagnetic R/V Kairei (KR05-17 dataset, JAMSTEC, Yokosuka, Japan). While direct field comparisons are complex due to differing times, locations, and vessel sizes, comparing platform-induced effects is informative as the fundamental hull susceptibility characteristics persist [7]. Applying Equation (3) revealed significantly more pronounced discrepancies between attitude-corrected and fully corrected anomalies for the ferromagnetic R/V Kairei (Figure S6b). This is attributed to the strong induced magnetization of its hull, quantitatively supported by Kairei's significantly higher susceptibility tensor compared to the paramagnetic USV, as estimated via Equation (3) (Tables 1 and S1). In contrast, these variations were relatively minor for the aluminium-alloy USV (Figure S6a), although applying Equation (3) shows that it still significantly improved stability and consistency relative to attitude changes.