Depth Conversion of Underwater Static Electric Fields for Submersibles in High-Latitude Low-Temperature Sea Areas

Depth conversion of underwater static electric fields refers to a mathematical approach that indirectly determines the distribution of planar electric fields at larger depths using measured planar electric field data obtained from a shallower region with finite depth and limited area. The complicated environment of high-latitude low-temperature sea areas further increases the difficulty of performing practical large-depth measurements of underwater electric fields. Therefore, depth conversion becomes an important technical strategy for overcoming the constraints of field measurements and for comprehensively understanding the distribution of underwater static electric fields of the target. This study begins with the mathematical formulation of the depth conversion problem, solves the related boundary value problem, and develops the corresponding depth conversion method. Subsequently, based on COMSOL simulation data of the underwater static electric field generated by a scaled-down submersible model, numerical analyses are conducted to investigate the effects of factors such as grid discretization, measurement plane dimensions, conversion depth, and data noise on the conversion accuracy. Finally, the reliability of the conversion method is validated in a laboratory environment by simulating a naturally frozen sea area and employing measured underwater static electric field data from the scaled-down submersible model. The results demonstrate that the developed conversion method can effectively achieve extrapolation of the underwater static electric field of the submersible from shallow regions to deeper water. Even when the noise amplitude is nearly twice that of the effective signal and the conversion depth reaches 8 times the outer diameter of the submersible, the relative root mean square error (RRMSE) of the conversion results can still be maintained below 0.10. These findings provide useful references for the advancement of technologies related to underwater electric field characteristic recognition and electric field stealth performance evaluation in high-latitude low-temperature sea areas.