全球定位系统2026，Vol.51Issue(4)：10-17,8.DOI:10.12265/j.gnss.2026199
电离层-空气-海水介质中水下VLF电磁波传播的HIE-FDTD方法
HIE-FDTD method for underwater VLF electromagnetic wave propagation in ionosphere-air-seawater media
摘要
Abstract
The study of underwater very low frequency(VLF)electromagnetic wave propagation in ionosphere-air-seawater media is of great significance for cross-air-sea interface communication.For the fine-layered structure,the conventional finite-difference time-domain(FDTD)method was limited by the minimum grid size,making it difficult to increase the time step.In this paper,the hybrid implicit-explicit finite-difference time-domain(HIE-FDTD)method was proposed to predict the propagation characteristics of underwater VLF electromagnetic waves in ionosphere-air-seawater media.Iteration formulas of the HIE-FDTD method for dispersive media in the perfectly matched layer(PML)absorbing boundary were derived in cylindrical coordinates.A propagation model for electromagnetic waves radiated from an underwater VLF source in the three-layer ionosphere-air-seawater medium was constructed.The influence of ionospheric variations on underwater and above-water propagation was revealed.The results show that the HIE-FDTD method achieves comparable accuracy to the conventional FDTD method,with significantly improved efficiency.Underwater VLF waves radiated from a source attenuate severely and are almost unaffected by the ionosphere,while their propagation in the above-water air is significantly modulated by the ionosphere.Strong absorption by the daytime ionospheric D-layer leads to increased signal attenuation,whereas the disappearance of the D-layer at night significantly improves propagation conditions.During the day-night transition,gradual changes in ionospheric parameters cause mode coupling and conversion,resulting in significant oscillations and non-uniform attenuation of the field strength distribution.关键词
甚低频(VLF)电磁波传播/时域有限差分(FDTD)/混合隐式-显式时域有限差分(HIE-FDTD)/完全匹配层(PML)/色散介质Key words
very low frequency(VLF)electromagnetic wave propagation/finite-difference time-domain(FDTD)/hybrid implicit-explicit finite-difference time-domain(HIE-FDTD)/perfectly matched layer(PML)/dispersive media分类
信息技术与安全科学引用本文复制引用
王丹丹,徐凱华,孔文君,王东,李维新,蒲玉蓉..电离层-空气-海水介质中水下VLF电磁波传播的HIE-FDTD方法[J].全球定位系统,2026,51(4):10-17,8.基金项目
国家自然科学基金重点项目(U2341201) （U2341201）
国家自然科学基金面上项目(62571216) （62571216）
国家自然科学基金青年科学基金(62201326) （62201326）
山东省青年科技人才托举工程(SDAST2025QTA008) （SDAST2025QTA008）
山东省高等学校青年创新团队(2025KJH090) （2025KJH090）
